Translate boundary conditions into Mathematica's code?

Hi,
I have been trying to find clues from Mathematica’s Documentation Centre as well as from the online lectures on how to translate a number of special boundary conditions onto Mathematica’s work sheet. I have been working on PDEs, in particular the reaction-diffusion system. To those experts in the language, I would really like your help on this matter. The problem is on Boundary Condition 4 (B.C.4), as well as B.C. 2 and 3, since the space, z is a function of time. The system of equations is attached together with this post. It is just the boundary conditions section that I’m confused with.

Thanks guys.
HU.

The forum rules are that you cannot post pictures of equations, please read the forum rules.

You should see examples of everyting in your equations by seeing:

I can’t read all of your equations but feel they are typical. You will see quickly how to type them in and see solution graphing having read the URL above.

Hi John,
I am so sorry about the picture of equations. I just encountered that I could use Mathematica Cloud Notebook to write equations. Will use that later in other discussions. Will definitely look at NDSolve in the Wolfram reference again. Thanks for the comment and suggestion, really appreciate them.
HU.